Oil Pressure Gauge Bouncing Around

Oil pressure that goes up a bit as rpm increases, and falls a bit as rpm decreases, is normal. Bouncing around, however, not so much. That suggests air bubbles in the line, which brings up the question "have you checked the dip stick lately."

Had a car once that would show 20 psi at idle, and as you drove off, the oil pressure would rise to about 40 psi, and stay there because there was a pressure relief valve regulating it. As you came to a stop, it would drop off again back to 20.